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Answer:

x = 4 and y = 9

Step-by-step explanation:

Let x and y be the two numbers. Also,

Let the first number be x and the second number be y.

Converting the word expressions to an equation we get:

                   y = x + 5

               3x + 2y = 30

Only thing left is to substitute y = x + 5 into the second equation

     3x + 2y = 30

     3x + 2(x + 5) = 30   (substituting y as x + 5)

     3x + 2x + 10 = 30   (multiplying by both x and 5)

     5x = 30 - 10     (collecting like terms to one side)

     5x = 20

     \(\frac{5x}{5} = \frac{20}{5}\)     (divide both sides by 5 to get the value of x)

     x = 4

 Now that we know the value of x, we can find y.

      y = x + 5

      y = 4 + 5

      y = 9

If you want to make sure your answer is correct, substitute x and y into the equation.

  3x + 2y = 30

  3(4) + 2(9) = 30

  12 + 18 = 30

  30 = 30

Answer:

$763,808.48

Step-by-step explanation:

765,000 - (4,697.77 - (765,000 * .055/12)) =

$763,808.48

Using Absolute Maximum and Minimum,

the absolute Maximum value of f(x) is 8.5 at x = 8 and absolute minimum value of f (x) is 2.44 at x = 0.2 on given interval [0. 2, 8].

we have given function is

f(x) = x + 4/x ---(1)

and interval [ 0.2 , 8]

firstly, find first order derivative of f(x)

f'(x) = 1 - 4/x²

now, f'(x) = 0 then 1 - 4/x^2 =0

=> 4/x²= 1

=> x² = 4

=> x = 2 or -2

that is 2 and -2 are critical points but only critical number 3 belong to given closed interval.

we evaluate the value of "f" at critical point, x =3 and at ends points of given interval [0.2, 8].

f(3) = 3 + 4/3 = 4.33 , f(0.2) = 0.2 + 4/0.2 = 2.44

, f(8) = 8 + 4/8 = 17/2 = 8.5

Hence, the absolute Maximum value of f on [0.2,8] is 8.5 occuring at x = 8 and absolute minimum value of f on [0.2,8] is 2.44 occuring at x= 0.2 ..

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\( - 9x + 3y - 27 = 0 \\ a = - 9 \\ b = 3 \\ c = 0 \\ {b}^{2} - 4ac = 9 - 4( - 9)( - 27) = 0 \\ x = \frac{ - b}{2a} = \frac{ - 3}{ - 18} = \frac{1}{6} \\ x = \frac{1}{6} \\ y = ( - 9 \times \frac{1}{6} ) + 3y = 27 \\ \frac{ - 3}{2} + 3y = 27 \\ 3y = 27 + \frac{3}{2 } \\ 3y = \frac{57}{2} \\ y = \frac{57}{6} = \frac{19}{2} \\ \)

i hope it helps u.....

This means that we can find the number 3 in either 2 or 3 operations, depending on the steps taken during the binary search.

To find the number 3 located at the 1st position in the list {3, 37, 45, 57, 93, 120}, we can use binary search algorithm. In each step, we divide the list in half and check if the middle element is equal to 3. If not, we continue searching in the appropriate half until we find the number.

In this case, since the list has 6 elements, we can find the number 3 in at most log2(6) = 2.585 operations. This means that we can find the number 3 in either 2 or 3 operations, depending on the steps taken during the binary search.

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To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.

Given:

f(x, y) = xy

Partial derivative with respect to x (keeping y constant):

∂f/∂x = y

Partial derivative with respect to y (keeping x constant):

∂f/∂y = x

So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):

∇f(4, 7) = (7, 4)

The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:

z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)

Substituting the values:

z - 28 = (7, 4) · (x - 4, y - 7)

Expanding the dot product:

z - 28 = 7(x - 4) + 4(y - 7)

z - 28 = 7x - 28 + 4y - 28

z = 7x + 4y - 56

Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.

To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.

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The remainder when a 90-digit number 9999 is divided by 89 is 0, as the result of applying the divisibility rule of 89, which involves reversing the digits of the number and subtracting the smaller from the larger.

To find the remainder when a 90-digit number 9999 is divided by 89, we can use the divisibility rule of 89. The rule states that for any integer n, the number obtained by reversing the digits of n and subtracting the smaller from the larger is divisible by 89.

In this case, we reverse the digits of 9999 to get 9999 again, and subtract the smaller from the larger to get 0. Since 0 is divisible by any number, including 89, the remainder when 9999 is divided by 89 is 0.

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Answer:

x + 49 + 28 = 180

Step-by-step explanation:

The angle adjacent to x on the left is vertically opposite 49° and is congruent.

The 3 angles then lie on a straight line and sum to 180° , that is

x + 49 + 28 = 180

Step-by-step explanation:

Tranversal-(two parallel angles are cut by a third)

The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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Answer:

15.05

Step-by-step explanation:

Answer:

Step-by-step explanation:

The tables are illustrations of logarithmic and exponential functions

The functions are given as:

\(f(x) = b^x\) --- table I

\(g(x) = log_b(x)\) --- table II

The above equations mean that:

Tables I and II are inverse functions

On the table II (see attachment), we have:

\(g(8) = 1.292\)

This means that:

\(f(1.292) = 8\)

Also, On the table I, we have:

\(f(1.544) = 12\)

This means that:

\(g(12) = 1.544\)

So, the missing values for both tables are 1.292 and 1.544

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A control chart is a visual representation of the various states in a process. The answer is b. True. Control charts are used in quality control and process improvement to monitor and analyze the performance of a process over time.

b. True. A control chart is a graphical tool used to monitor the performance of a process over time. It is a visual representation of the data collected from the process and helps in identifying any patterns or trends that may occur. The chart typically consists of a central line representing the average or target value, and upper and lower control limits representing the acceptable range of values for the process. The data is plotted on the chart, and any points that fall outside the control limits indicate a process that is out of control and may require further investigation. Control charts are commonly used in industries such as manufacturing, healthcare, and finance to ensure that processes are running smoothly and to identify any potential issues early on. Overall, control charts provide a powerful way to monitor and manage processes in a systematic manner.

They help to identify trends, patterns, and variations that may indicate potential issues, allowing for timely corrective actions to be taken.

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We first determine the two elements as "(u = 3x - 1") and "(v = 5 - x") in order to estimate the derivative of the given function, "(y = (3x - 1)(5 - x)" using the product rule.

According to the product rule, if "y = u cdot v," then "y' = u cdot v + u cdot v'" gives the derivative of "y" with regard to "x."

When we use the product rule, we discover:

\(u' = 3\) (v' = -1 is the derivative of (u) with respect to (x)) ((v's) derivative with regard to (x's))

When these values are substituted, we get:

\(y' = (3x - 1)'(5 - x) + (3x - 1)(5 - x)'\)

\(y' = 3(5 - x) + (3x - 1)(-1)\)

Simplifying even more

\(y' = 15 - 3x - 3x + 1\)

\(y' = -6x + 16\)

The derivative at (x = 6) is evaluated by substituting (x = 6) into the

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Specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.

What is a Variable?

A variable is a quantity that can change in the context of a mathematical problem or experiment. We usually use one letter to represent a variable. The letters x, y, and z are common general symbols used for variables.

The procedure for identifying or indicating the value of cases on a variable is commonly known as data coding or data labeling. It involves assigning specific numerical or categorical values ​​to represent different categories or levels of a variable.

Here is the general procedure for encoding variables:

Define the variable: Start by clearly defining the variable you want to code. Understand its nature (eg nominal, ordinal, interval or ratio) and the categories or levels it covers.

Determine the encoding scheme: Decide on the encoding scheme you will use to represent the variable. For nominal variables (categories without their own order), you can assign numbers or labels to each category. For ordinal variables (categories with a meaningful order), you can assign numbers or labels that reflect the order. For interval or ratio variables, the numerical values ​​themselves can indicate the value of the variable.

Assign Codes: Assign specific codes or labels to represent each category or level of the variable. These codes can be numbers, letters, or any other symbol you choose. Make sure the codes are unique and do not overlap.

Apply Coding: Apply assigned codes to matching cases or observations in your dataset. Depending on the software or tool you are using, there are different ways to do this. You can manually enter codes, use syntax or programming commands, or use data transformation functions.

Verify your coding: Double-check your coding to ensure accuracy. Review a sample of the coded cases to ensure they match the intended coding scheme. This step is essential to avoid errors and inconsistencies in your data.

It is important to note that specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.

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Answer:

I would say the 3rd one, i think

Step-by-step explanation:

After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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the equation for a rational function with the given characteristics calculator is y = -10 (x - 1)² / (x - 2)

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomial coefficients don't have to be rational numbers; they can be taken in any field. K

Vertical asymptote at, x = 2

So, (x - 2) will be in the denominator

Double zero at x = 1

So, (x - 1)² will be in the numerator.

So, y = a (x - 1)² / (x - 2)

at x = 0, y = 5

So, 5 = a (-1)² / (-2)

Therefore, a = -10

So, y = -10 (x - 1)² / (x - 2)

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COMPLETE QUESTION:

Write an equation for a rational function with the given characteristics. Vertical asymptote at x = 2, double zero at x = 1, y-intercept at (0,5)

y =

Answer:

Rise over Run

Step-by-step explanation:

Start to count up and count across the graph so like

^ then ——>

|

To calculate the value of X that Ellen should deposit in the bank, we need to determine the present value of the future payments that will accumulate to $50,000 in six years.

Using the formula for compound interest, the present value can be calculated as follows:

PV = X/(1 + r)^1 + X/(1 + r)^2 + X/(1 + r)^3,

where r is the annual interest rate (5%) expressed as a decimal.

To find the value of X, we set the present value equal to $50,000 and solve for X:

50,000 = X/(1 + 0.05)^1 + X/(1 + 0.05)^2 + X/(1 + 0.05)^3.

Once we determine the value of X, we can proceed to the next step.

For the second part of the question, after four years, the bank raises the interest rate to 6%.

From year four to year six, Ellen's money will continue to accumulate interest.

To find the amount donated, we calculate the future value of the remaining amount after deducting the down payment of $50,000:

Remaining amount = X/(1 + 0.06)^2 + X/(1 + 0.06)^3 + X/(1 + 0.06)^4.

The donated amount is then the difference between the remaining amount and the total accumulated after six years.

By evaluating these expressions, we can determine the value of X and the amount donated by Ellen.

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Answer:

Statement 2: m∠ ELD = (2x)°

Reason 4: Sum of angles on a straight line is equal to 180°

Statement 6: 2x = 56

Step-by-step explanation:

Since the first step talks about we being given m∠ ELG = 124°, the next thing we are given in the question is that; m∠ ELD = (2x)°

In statement 4,it is written that;

m∠ ELD + m∠ ELG = 180°

The reason behind this is that;

Sum of angles on a straight line is equal to 180°.

For reason 6, we are told it is a subtraction property.

Now the preceding statement gave us;

2x + 124 = 180

Which means that for subtraction property here, we will have;

2x = 180 - 124

2x = 56

Yes , Are collinearity and betweenness of points maintained under rotation.

A rotation is a transformation that maintains congruence of the original figure and its image.

What does "collinearity" mean?

What is an example of collinearity?

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To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

60 goody bags

Step-by-step explanation:

1 kg = 1000 g

6.2 kg = 6,200 g

Empty box = 200 g

Box + goody bags = 6,200 g

Weight of Goody bags = Box + goody bags - empty box

= 6,200g - 200g

= 6,000 grams

Each goody bag = 100 g

how many goody bags are inside the box

Number of goody bag in the box = total weight of goody bag / weight of each goody bag

= 6,000 grams / 100 grams

= 60 goody bags

There are 60 goody bags in the box

The actual calculation depends on the specific vector field you are working with. You need to substitute the appropriate expressions for P and Q into the integrals and evaluate them accordingly.

To evaluate the line integral around the clockwise-oriented triangle with corners at the origin (0,0), (1,0), and (0,1), we need to sketch the vector field and the triangle and then calculate the integral.

Next, let's assume there is a vector field defined over the plane. Since you haven't provided the vector field explicitly, let's use a general notation and consider a vector field F = (P, Q), where P and Q are functions of x and y.

To calculate the line integral, we need to parameterize the triangle. We can divide the triangle into three line segments and parametrize each segment separately.

Line segment from (0,0) to (1,0):

Let's parameterize this segment as r(t) = (t, 0), where 0 ≤ t ≤ 1.

Line segment from (1,0) to (0,1):

Let's parameterize this segment as r(t) = (1 - t, t), where 0 ≤ t ≤ 1.

Line segment from (0,1) to (0,0):

Let's parameterize this segment as r(t) = (0, 1 - t), where 0 ≤ t ≤ 1.

Now, we can calculate the line integral for each segment and sum them up:

Line integral along the first segment:

\(\int(0 to 1) P(t, 0) dt + \int(0 to 1) Q(t, 0) dt\)

Line integral along the second segment:

\(\int(0\: to \:1) P(1 - t, t) dt + \int(0 \:to\: 1) Q(1 - t, t) dt\)

Line integral along the third segment:

\(\int(0 \:to \:1) P(0, 1 - t) dt + \int(0\: to \:1) Q(0, 1 - t) dt\)

Finally, the total line integral around the triangle is the sum of these three line integrals:

Total Line Integral = Line integral of segment 1 + Line integral of segment 2 + Line integral of segment 3

Please note that the actual calculation depends on the specific vector field you are working with. You need to substitute the appropriate expressions for P and Q into the integrals and evaluate them accordingly.

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